The field of vibration-based structural health monitoring involves recording a structure's dynamic response to applied or ambient excitation and then extracting damage-induced signatures from the data. These features (e.g., modal properties) are then tracked as damage is incurred to the structure. By continually comparing newly acquired features to a baseline set, ideally extracted from a healthy (or unimpaired) structure, the practitioner makes confidence-based judgments as to whether the structure is damaged. The main problem with this approach is that variations in feature values due to effects other than damage, e.g., temperature and humidity will frequently “mask” damage-induced changes.
Damage in structures often manifests itself as a nonlinearity while most “healthy” structures are well described by a linear model. Detecting damage-induced nonlinearities in structural response data is therefore an effective damage detection strategy. Many of the commonly used approaches in damage detection, however, were designed for analyzing linear system dynamics. In a statistical sense, these approaches make the assumption that the covariance matrix captures the necessary dynamical relationships (correlations) among the data. The linear auto- and cross-correlation functions, the auto- and cross-spectral densities (by the Weiner-Khinchine relationship), and the frequency response function are defined by second-order statistics. These algorithms comprise traditional modal analysis and are ideal if the system being studied is accurately described by a linear mode. Indeed, for linear systems, the auto- and cross-spectral densities sufficiently described the dynamical relationship(s) among the data.
For nonlinear systems, where higher-order correlations become important, these tools are not well suited. Nonetheless, traditional modal analysis can be adapted to account for nonlinearity. See e.g., Worden K. et al., 2001 Nonlinearity in experimental modal analysis, Philosophical Transactions of the Royal Society of London—Series A, vol. 359, pp. 113-130, incorporated herein by reference. For example, if the form of the nonlinearity is known a priori the practitioner might look for specific frequency domain ‘distortions’. Similarly, if baseline data have been collected with the structure in a known (or assumed) linear state, subsequently collected data may be analyzed for the appearance of additional poles in the frequency domain, the assumption being that the changes are due to the presence of a nonlinearity. Perhaps the most straightforward approach is to apply variable amplitude loading and check the frequency response for dependences on the level of excitation. This approach was employed by Neild et al. in looking for damage in concrete beams. See e.g., Neild et al., 2003 Nonlinear vibration characteristics of damaged concrete beams, Journal of Structural Engineering, vol. 129, pp. 260-268, incorporated herein by reference. For complex structures, an accurate model of the nonlinearity may be difficult to acquire, and without such a model, it may not be readily apparent what nonlinear feature to expect. Furthermore, many situations call for the practitioner to retro-fit an existing structure (no baseline data present). Exciting a structure with variable amplitude inputs may pose further practical challenges.